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<meta name="description" content="第二章 线性表线性表：表内数据类型相同，有限序列 本章将以总结的形式展现： 2.1 顺序表与链式表的区别     顺序表 链式表     存取 随机存取 顺序存取   结构 顺序存储（连续） 随机存储（不连续）   空间分配 静态存储（可以动态分配） 动态存储   操作 查找 O(1) ,插入和删除O（n） 查找 O(n) ,插入和删除O（1）   缺点 插入删除不便，长度不可以改变 查找速度慢，">
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<meta property="og:description" content="第二章 线性表线性表：表内数据类型相同，有限序列 本章将以总结的形式展现： 2.1 顺序表与链式表的区别     顺序表 链式表     存取 随机存取 顺序存取   结构 顺序存储（连续） 随机存储（不连续）   空间分配 静态存储（可以动态分配） 动态存储   操作 查找 O(1) ,插入和删除O（n） 查找 O(n) ,插入和删除O（1）   缺点 插入删除不便，长度不可以改变 查找速度慢，">
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        <h1 class="article-title">神经网络-下</h1>
    
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        <ol class="toc"><li class="toc-item toc-level-1"><a class="toc-link" href="#M-P%E7%A5%9E%E7%BB%8F%E5%85%83%E5%92%8C%E6%84%9F%E7%9F%A5%E6%9C%BA%E5%9B%9E%E9%A1%BE"><span class="toc-text">M-P神经元和感知机回顾</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E7%A5%9E%E7%BB%8F%E7%BD%91%E7%BB%9C%E4%BB%A5%E5%8F%8A%E7%AE%97%E6%B3%95"><span class="toc-text">神经网络以及算法</span></a></li><li class="toc-item toc-level-1"><a class="toc-link" href="#%E5%B0%8F%E7%BB%93"><span class="toc-text">小结</span></a></li></ol>
    
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        <p><strong><em>图片显示不出来可刷新</em></strong></p>
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<h1 id="M-P神经元和感知机回顾"><a href="#M-P神经元和感知机回顾" class="headerlink" title="M-P神经元和感知机回顾"></a>M-P神经元和感知机回顾</h1><p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162530.png" alt=""></p>
<p>　　<img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162446.png" alt=""></p>
<p>其中θ为我们之前提到的神经元的激活阈值，函数f(·)也被称为是激活函数。如上图所示，函数f(⋅)可以用一个阶跃方程表示，大于阈值激活；否则则抑制。但是这样有点太粗暴，因为阶跃函数不光滑，不连续，不可导，因此我们更常用的方法是用sigmoid函数来表示函数函数f(⋅)。</p>
<p>​       感知机（perceptron）是由两层神经元组成的结构，输入层用于接受外界输入信号，输出层（也被称为是感知机的功能层）就是M-P神经元。下图表示了一个输入层具有三个神经元（分别表示为x0x0、x1x1、x2x2）的感知机结构：</p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162550.png" alt=""></p>
<p>根据上图不难理解，感知机模型可以由如下公式表示：</p>
<script type="math/tex; mode=display">
y=f(wx+b)</script><p>​    其中，w为感知机输入层到输出层连接的权重，b表示输出层的偏置。事实上，感知机是一种判别式的线性分类模型，可以解决与、或、非这样的简单的线性可分（linearly separable）问题。</p>
<p>参考：(<a target="_blank" rel="noopener" href="http://www.cnblogs.com/maybe2030/p/5597716.html">http://www.cnblogs.com/maybe2030/p/5597716.html</a></p>
<h1 id="神经网络以及算法"><a href="#神经网络以及算法" class="headerlink" title="神经网络以及算法"></a>神经网络以及算法</h1><p>说到神经网络，大家看到这个图应该不陌生：</p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162621.png" alt=""></p>
<p>　　这是典型的三层神经网络的基本构成，Layer L1是输入层，Layer L2是隐含层，Layer L3是隐含层，</p>
<p>我们现在手里有一堆数据{x1,x2,x3,…,xn},输出也是一堆数据{y1,y2,y3,…,yn},现在要他们在隐含层做某种变换，让你把数据灌进去后得到你期望的输出。如果你希望你的输出和原始输入一样，那么就是最常见的自编码模型（Auto-Encoder）。可能有人会问，为什么要输入输出都一样呢？有什么用啊？其实应用挺广的，在图像识别，文本分类等等都会用到</p>
<p>​       本文直接举一个例子，带入数值演示反向传播法的过程（注：本文假设你已经懂得基本的神经网络构成，如果完全不懂，可以参考Poll写的笔记：])）</p>
<p>　　假设，你有这样一个网络层：</p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162644.png" alt=""></p>
<p>　　第一层是输入层，包含两个神经元i1，i2，和截距项b1；第二层是隐含层，包含两个神经元h1,h2和截距项b2，第三层是输出o1,o2，每条线上标的wi是层与层之间连接的权重，激活函数我们默认为sigmoid函数。</p>
<p>　　现在对他们赋上初值，如下图：</p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162724.png" alt=""></p>
<p>　　其中，输入数据  i1=0.05，i2=0.10;</p>
<p>　　　　　输出数据 o1=0.01,o2=0.99;</p>
<p>　　　　　初始权重  w1=0.15,w2=0.20,w3=0.25,w4=0.30;</p>
<p>　　　　　　　　　  w5=0.40,w6=0.45,w7=0.50,w8=0.55</p>
<p>　　目标：给出输入数据i1,i2(0.05和0.10)，使输出尽可能与原始输出o1,o2(0.01和0.99)接近。</p>
<p>　　<img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162742.png" alt=""></p>
<p>　　<img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162804.png" alt=""></p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824162836.png" alt=""></p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824163047.png" alt=""></p>
<p>现在我们来分别计算每个式子的值：</p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824163115.png" alt=""></p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824163134.png" alt=""></p>
<p><img src="https://images2015.cnblogs.com/blog/853467/201606/853467-20160630153103187-515052589.png" alt="img"></p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824163635.png" alt=""></p>
<p><img src="https://images2015.cnblogs.com/blog/853467/201606/853467-20160630153614374-1624035276.png" alt="img"></p>
<p>（其中，<img src="https://images2015.cnblogs.com/blog/853467/201606/853467-20160630153700093-743859667.png" alt="img">是学习速率，这里我们取0.5）</p>
<p>同理，可更新w6,w7,w8:</p>
<p><img src="../../../../../AppData/Roaming/Typora/typora-user-images/1566635906687.png" alt="1566635906687"></p>
<p>3.隐含层——&gt;隐含层的权值更新：</p>
<p>　方法其实与上面说的差不多，但是有个地方需要变一下，在上文计算总误差对w5的偏导时，是从out(o1)——&gt;net(o1)——&gt;w5,但是在隐含层之间的权值更新时，是out(h1)——&gt;net(h1)——&gt;w1,而out(h1)会接受E(o1)和E(o2)两个地方传来的误差，所以这个地方两个都要计算。</p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824163850.png" alt=""></p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824163916.png" alt=""></p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824163942.png" alt=""></p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824164021.png" alt=""></p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824164103.png" alt=""></p>
<p>同理，额可更新w2,w3,w4的权值：</p>
<p><img src="https://moluggg.oss-cn-qingdao.aliyuncs.com/img/20190824164120.png" alt=""></p>
<p>　　这样误差反向传播法就完成了，最后我们再把更新的权值重新计算，不停地迭代，在这个例子中第一次迭代之后，总误差E(total)由0.298371109下降至0.291027924。迭代10000次后，总误差为0.000035085，输出为<a href="原输入为[0.01,0.99]">0.015912196,0.984065734</a>,证明效果还是不错的。</p>
<pre><code class="lang-python">import numpy as np
import matplotlib.pyplot as plt
import math

x=np.array([0.05,0.10])#数值
y=np.array([[0.15,0.25],[0.2,0.3]])#权重
y1=np.array([[0.4,0.5],[0.45,0.55]])#第二层权重
r=np.array([0.01,0.99])#期望输出

b=0.35
b1=0.6
q=0.5#学习率

def neth(x,y,b):
    return np.dot(x,y)+b     #将权重与数值相乘
##np.dot()   一维矩阵相乘得到內积，多维就是离散课上见得方法，扫射。

def outh():

    outh=[]

    for i in range(len(y[0])):

        a=1/(math.exp(-neth(x,y,b)[i])+1)# sigmoid函数

        outh.append(a)##

    return np.array(outh)

def neto():

    return np.dot(outh(),y1)+b1

def outo():

    outo=[]

    for i in range(len(y1[0])):

        a=1/(math.exp(-neto()[i])+1)

        outo.append(a)

    return np.array(outo)
o=0
O=[]
result=[]
#梯度下降
while True:
    o=o+1
    dif=[[0,0],[0,0]]
    dif1=[[0,0],[0,0]]
      a=0
#对w5-w8进行求导
     for i in range(len(y1)):
        for j in range(len(y1[i])):
              dif1[i][j]=(-(r[j]-outo()[j]))*(outo()[j]*(1-outo()[j]))*(outh()[i])#公式
              y1[i][j]=y1[i][j]-q*dif1[i][j]
#对w1-w4进行求导
      for i in range(len(y)):
        for j in range(len(outo())):
              a=a+(-(r[j]-outo()[j]))*outo()[j]*(1-outo()[j])*y1[i][j]#公式
            for k in range(len(y[i])):
              dif[i][k]=a*(outh()[k]*(1-outh()[k]))*x[i]
      y[i][k]=y[i][k]-q*dif[i][k]
  e=np.sum((r-outo())**2/2)    #总误差
  result.append(e)
  O.append(o)
  if e&lt;0.00001:
    break
plt.plot(O,result)
plt.show()
print(outo())
print(o)
print(e)
</code></pre>
<h1 id="小结"><a href="#小结" class="headerlink" title="小结"></a>小结</h1><p>1.什么是感知器，神经元模型</p>
<p>2.动量因子又是什么？</p>
<p>3.B-P神经元反向传播过程，注意w5,w1不同</p>

      
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